电磁场与电磁波(必考题)

v1.0 可编辑可修改1())]43(cos[31,,z x t-e t z x H +=πωπy ωz x z k y k x k z y x ππ43+=++π3=x k 0=y k π4=z k)/(5)4()3(22222m rad k k k k zy x πππ=+=++=λπ2=k )(4.02m k==πλ cv f ==λ)(105.74.010388Hz cf ⨯=⨯==λ)/(101528s rad f ⨯==ππω)/(31),()43(m A e e z x H z x j y +-=ππ)/()243254331120),(),(),()43()43(m V ee e e e e e k k z x H e z x H z x E z x j z x z x z x j y n +-+--=+⨯⨯=⨯=⨯=πππππππηη（()[])/()43(cos 2432),,(m V z x t e e t z x E z x +--=πω())]43(cos[31,,z x t-e t z x H +=πωπy ()[]()[])/()43(cos 322431)]43(cos[31)43(cos 243222m W z x t e e z x t-e z x t e e H E S z x z x +-+=+⨯+--=⨯=πωππωππωy ())43(2432),(z x j z x e e e z x E +--=π)43(31),(z x j y e e z x H +-=ππ()())/(322461312432Re 21Re 212*)43()43(*m W e e e e e e e H E S z x z x j y z x j z x av +=⎪⎭⎪⎬⎫⎪⎩⎪⎨⎧⎥⎦⎤⎢⎣⎡⨯-=⎪⎭⎫ ⎝⎛⨯=+-+-ππππz00x φ==0x a φ==00001(,)()()(sin cos )(sinh cosh )(3)nnnn n n n n n x y A x B C y D A k x Bk x C k y D k y φ∞==+++++∑(0,)0(0)y y b φ=≤<00010()(sinh cosh )n n n n n n B C y D B C k y D k y ∞==+++∑y0b→0(0,1,2,)n B n ==0001(,)()sin (sinh cosh )n n n n n n n x y A x C y D A k x C k y D k y φ∞==+++∑(,)0(0)a y y b φ=≤<00010()sin (sinh cosh )n n n n n n n A a C y D A k a C k y D k y ∞==+++∑y 0b→00A =sin 0(1,2,)n n A k a n ==nA 0φ≡sin 0n k a = (1,2,)n n k n aπ==1(,)sin(sinh cosh )n n n n n x n y n y x y A C D a a aπππφ∞==+∑(,0)0(0)x x a φ=≤≤10sinn n n n x A D aπ∞==∑ 0a →0n A ≠0(1,2,)n D n == 1(,)sin sinh nn n x n yx y A a aππφ∞='=∑nn n A A C '= 0(,)(0)x b U x a φ=≤≤01sin sinh nn n x n b U A a aππ∞='=∑nA '(0,)a sin n x a π⎧⎫⎨⎬⎩⎭01sinn n n x U f aπ∞==∑ 002sin a n n xf U dx a aπ=⎰041,3,5,02,4,6,U n n n π⎧=⎪=⎨⎪=⎩sinh n nf A n b a π'=041,3,5,sinh 02,4,6,U n n b n a n ππ⎧=⎪⎪=⎨⎪=⎪⎩1,3,41(,)sinsinh sinhn U n x n yx y n b a an aππφππ∞==∑)0(0),0(b y y <≤=ϕ)0(0),(b y y a <≤=ϕ)0(0)0,(a x x ≤≤=ϕ)0(),(0a x Ub x ≤≤=ϕ02=∇ϕv1.0 可编辑可修改2()z j 0e E t ,z β-=x e Ezj x i e E β-=0zj yzj x z i eE eE ββηη--=⨯=00101ηη=200002ηεηεεμη===rr 3122001212-=+-=+-=ηηηηηηηηΓ322222000122=+⨯=+=ηηηηηητ z j x zj x r e E eE ββ0031-==Γz j y z j x z r z r e E e E H ββπηη36031)(1)(10000=⎪⎭⎫⎝⎛-⨯-=⨯-=βεεμωβ2002==rz j xz jk x t e E e E βτ200322--== z j y z j x z t z t e E e E ββπηη2020229032)(1)(1--=⎪⎭⎫⎝⎛⨯=⨯=0100133j z j z j z j z x x x E E e E e e e e E e e ββββ--⎡⎤=-=-⎢⎥⎣⎦0021122cos 33333j z j z j z j z x x e E e e e e E e z βββββ---⎡⎤⎡⎤=--=-⎢⎥⎢⎥⎣⎦⎣⎦000111203601203j z j z j z j z yy yE E E H e e e e e e e ββββπππ--⎡⎤=+=+⎢⎥⎣⎦0021122sin 12033312033j z j z j z j z yy E E e e e e e e j z βββββππ---⎡⎤⎡⎤=-+=+⎢⎥⎢⎥⎣⎦⎣⎦231131111=-+=-+=ΓΓS()z j e E z β-=0x i ()zj e E z β-=0x i z j yz j x z i e E e E ββηη--=⨯=001z j x z j x r e E e E ββ00)1(-=-=()zj yz j x z r z r e E e E ββπηη120)(1)(1000=-⨯-=⨯-=zE j e e E e e E e E E E x z j x z j x r i βββsin 20001-=-=+=-z Ee E e E H y z j y z j yr i βπππββcos 601201200001=+=+=-()ππ60600001Ee E e e H e J x yz z n s =⨯-=⨯==1100(,)Re 2sin cos 22sin sin j tx x E z t E e e E z t e E z tωπβωβω⎛⎫⎡⎤==- ⎪⎣⎦⎝⎭=⎪⎩⎪⎨⎧≥-=<=aa A a ρφρρϕρϕcos )(0221zue u e u e u z∂∂+∂∂+∂∂=∇ φρρφρ011=-∇=ϕφρφρϕφρϕρϕϕφρφρsin 1cos 1222222222⎪⎪⎭⎫⎝⎛-+⎪⎪⎭⎫ ⎝⎛+-=⎪⎪⎭⎫⎝⎛∂∂+∂∂+∂∂-=-∇=a A a A z e e e z()()φερρρρcos 22012A aan S -=⋅=-⋅===81=r εt cos E E m ω=t E E J m ωσcos 4==tE t E E D m m r ωεωεεεcos 81cos 00===09681sin 181102110sin 1.458sin 36D m m m DJ E t t E t E tεωωπωωπ-∂==-∂=-⨯⨯⨯⨯⨯=-1,25.2r r ==με())t-kz cos(40t ,z ωx e E=v S a)/(102101022109s rad f ⨯=⨯⨯==πππω880010225.210311⨯=⨯=====rrcv f εεεμμελ)(02.0101010298m f v =⨯⨯==λ)/(10002.022m rad k ππλπ===)/(40)(m V e e z E jkz x -=)(8025.2120000Ωππεηεεμεμη=====r r 140()()801(/)2jkzz yjkzyH z e E z e e e e A m ηππ--=⨯==)/()cos(21),(m A kz t t z y-=ωπ**2111Re Re 4022210(/)jkz jkz av x y zS E H e e e e e W m ππ--⎡⎤⎛⎫⎡⎤=⨯=⨯⎢⎥ ⎪⎢⎥⎣⎦⎝⎭⎢⎥⎣⎦=v1.0 可编辑可修改32z 2y 2x z e xy e x e A++=A ⋅∇z xy x 222++A ⨯∇2y zzxy x zA y A x A zy x 222++=∂∂+∂∂+∂∂=⋅∇222)(y x xy xy y A y z z yy y =∂∂∂∂∂∂⨯∇B A、0=⋅0=σ∞→σσ=E22z3x y 2+==E ()642z y x ++-()zxy y z y x z y x z y x 6422++-=⎪⎪⎭⎫ ⎝⎛∂∂+∂∂+∂∂-=-∇=ϕϕϕϕB A⨯∇=0=⋅∇ερϕ/2-=∇02=∇ϕD E、()021=-⨯n ()21=-⋅n HB、()021=-⋅n ()021=-⨯n)4(2r =ε4e 2e e E z y x 1 ++==2E12z y x e e e ++ z z y x E e e e E 222 ++=1422200=⇒=⨯z z r E E εεε122z y x e e e ++=1ρ1B12πρμφI 2ρ2B 202πρμφIz 4e my e x e B z y x ++=0=∂∂+∂∂+∂∂=⋅∇zB y B x B zy x 5041-=⇒=++m ma 04πε()a 102εεπ+24επQr E r =⨯204rQ E r πε=aQ dr E U ar 04πε==⎰∞a UQC 04πε==Qr D r D r r =+222122ππ1201εεrrD D =()210012rQD r εεπε+=()210122r Q D r εεπε+=()210212r QE E rr εεπ+==aQdr E U ar )(2101εεπ+==⎰∞a UQC )(210εεπ+==πμ8nπα=D E、⋅21)2cos(20kz t e E x -=πDJ ()kz t x --ππε2sin 400[])2sin(40)2cos(2000kz t kz t tt x x D --=-∂∂=∂∂=ππεπεE022=+∇k c)(120Ωπ)/100.3(8s m c ⨯≈)/(2m rad π)(60Ωπ)/(105.18s m ⨯)/(4m rad πεμη=Ωμε1=v v f =λλπ2=k)(1200Ωπη=)/(1038s m c v ⨯≈=z j y x i e e j e (E E β--=)0z+ymxm E E =0=x φ2πφ-=y 02<-=-=πφφφx y ∆81=r ε181728110361101242990<=⨯⨯⨯⨯⨯==-ππεεπσωεσr fεμσ、、μσπf 4/πμσπf 1τ=+Γ10,25.2μμε==rπηη12001==ππεηεμη8025.212020222====r 2.01212-=+-=ηηηηΓ5.111=-+=ΓΓSi r θθ=t i k k θθsin sin 21==c θ12arcsin εε=b θ12arctanεεv1.0 可编辑可修改41>>kr λ>>r1．()021=-⋅J J e n ()021=-⨯E E e n nn J J 21=t t E E 21=212211221121////tan tan σσσσθθ===n n n t n t J J E E E E∞→1σ02→θ⎰⎰⋅=⋅SCd d ⎰⎰⎰⋅=⋅⨯∇=⋅SSCSd J S d H l d H =⨯∇⎰⋅=21l E d U UqC =ϕn∂∂ϕ⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧=⋅=⋅⋅∂∂-=⋅⋅∂∂+⋅=⋅⎰⎰⎰⎰⎰⎰⎰⎰dVd d d t d d t d d V S S S ρSS C C S D S B S B l E S DS J l H 0⎪⎪⎪⎪⎩⎪⎪⎪⎪⎨⎧=⋅∇=⋅∇∂∂-=⨯∇∂∂+=⨯∇ρD B BE D J H 0t t⎰⎰⎰⋅+⋅+⋅=⋅⨯-V V S V V t d d )2121(d d d )(J E B H D E S H E⎰⋅+⋅V V t d )2121(d d B H D E⎰⋅VVd J E⎰⋅⨯-SS H Ed )(0=Γ1=S 1||=Γ∞=S 1||0<<Γ∞<<S 1v1.0 可编辑可修改5。